Given three non-negative integers x, y and bound, the task is to print all the powerful integer ≤ bound in sorted order.
A powerful integer is of the form xi + yj for all i, j ≥ 0.
Input: x = 3, y = 5, bound = 10
Output: 2 4 6 8 10
30 + 50 = 1 + 1 = 2
30 + 51 = 1 + 5 = 6
31 + 50 = 3 + 1 = 4
31 + 51 = 3 + 5 = 8
32 + 50 = 9 + 1 = 10
Input: x = 2, y = 3, bound = 10
Output: 2 3 4 5 7 9 10
Approach: Initialize i = 0 for outer loop and j = 0 for inner loop, if xi = bound then break out of the outer loop (as adding any power of y to it will make it out of the bound). If xi + yj > bound then break out of the inner loop and in every other iteration of the inner loop, save xi + yj in a set to maintain a distinct and sorted list of the powerful integers. Print the contents of the set in the end.
To avoid calculating the powers of y again and again, all the powers of y can be pre-calculated and stored in a vector.
Below is the implementation of the above approach:
2 3 4 5 7 9 10
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